Building simply on my small talk at that time conference, Scott Aaronson includes a blog publish about entropy and complexity that you ought to go read at this time. This is much like one I ve been considering myself, but more clever and original.
Back yet Scott did foolishly in the finish from the publish mention the faster-than-light neutrino business. Which obviously brought to questions, in reaction to one of these he said thusly:
Closed timelike curves appear in my experience to become a different order of strangeness from anything so far discovered in physics like maybe 1000 occasions stranger than relativity, QM, virtual contaminants, and black holes come up with. And That I do not know how you could have tachyonic neutrinos without getting CTCs too would anybody who accepts that possibility be kind enough to describe it in my experience
The issue Scott is alluding to is the fact that, in relativity, this is the rate-of-light barrier that stops contaminants (or anything) from zipping around and meeting themselves previously a closed loop in spacetime. On the diagram by which time stretches up and down and space flat, the potential pathways of sunshine from the event define light cones, and physical contaminants need to stay inside these light cones. Spacelike trajectories that leave the sunshine cones simply aren t permitted within the conventional method of doing things.
That which you do not see within this spacetime diagram is really a slice representing the world at one fixed time, because that type of factor is totally observer-dependent in relativity. Particularly, should you could move ahead a spacelike trajectory, there'd be experts who does insist that you're traveling backwards over time. When you will go faster than light, quite simply, you are able to go in some time and meet yourself previously. This really is Scott s reason behind skepticism concerning the faster-than-light neutrinos: should you open that door simply a crack, all hell breaks loose.
But relaxation easy! It doesn t always follow. Advocates tend to be more than ingenious enough to develop methods to allow contaminants to maneuver faster than light without allowing them to travel along closed curves through spacetime. One minor technical note: if some particle moves faster than light, this is not closed timelike curves that you should be concerned about, this is closed spacelike curves which physical contaminants move.
But we shouldn t always even be worried about that. The typical argument that faster than light suggests a chance to travel on the closed loop assumes Lorentz invariance but when we uncover a genuine FTL particle, the first guess ought to be that Lorentz invariance is damaged. (Not your only possible guess, but an acceptable one.) Consider, for instance, the presence of a heretofore unobserved fluid pervading the world having a well-defined relaxation frame, that neutrinos connect to but photons don't. Or perhaps a vector area concentrating on the same qualities. You will find other ways we're able to imagine some background that really picks out a frequent frame of reference, breaking Lorentz invariance automatically.
In the event that s true, the argument that FTL suggests closed loops through spacetime no more works. Even when neutrinos can sneak outdoors light cones, there might nonetheless be neutrino cones that they're still limited. These neutrino cones can be somewhat bit larger than regular light cones, however they could still define a set perception of moving forward over time that even neutrinos couldn t violate.
There s a pleasant (although technical) discussion of the inside a short paper by Robert Geroch. Read Section 2 for that math, Section 3 for that words. In the discussion:
In a nutshell, the causal cones of special relativity, out of this perspective, don't have any special place in addition to the cones associated with a other system. This really is democracy of causal cones having a vengeance. This, obviously, isn't the traditional view. That view the special relativity causal cones possess a preferred role in physics arises, I suspect, from the truth that many other systems electromagnetism, the spin-s elds, etc employ precisely individuals same cones his or her own. And, indeed, it might be the physical world is organized around this type of commonality of cones. However, it's feasible for there are a variety of others not observed (or possibly they've been!) that employ quite di erent teams of causal cones. And also the cones of those others would likely lie outdoors the null cones of special relativity, i.e., scalping strategies would likely manifest superluminal signals. None of the would contradict our fundamental ideas about how exactly physics is structured: A preliminary-value formulation, causal cones regulating signals, etc.
The possibilities still lengthy from the OPERA result being right at face value. But even when this is right, it doesn t immediately imply neutrinos are time-vacationers.
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